Making data instantly available is very important for nowadays industrial applications. The goal of this research is to provide database management schemes for distributed systems so that data can be efficiently accessed even if there are a lot of failures and busy sites in the distributed system.To achieve this goal, data are replicated at different sites of the system. Two schemes are presented to manage the replicated data, the triangular lattice scheme (18) and the new hierarchical quorum consensus scheme (17). It is proved that both schemes require access to the minimum number of data copies to maintain data consistency. This ensures that data can be efficiently accessed. In addition, both schemes offer asymptotically high availability. Thus data are available even if there are a lot of failures and busy sites in the system. The triangular lattice scheme has the advantage that the data access cost increases gradually as the number of failures and busy sites increases. The new hierarchical quorum consensus scheme has the advantage that the system designer can control the data availability and efficiency by adjusting parameters.Software has been implemented to simulate a distributed database system and to compare the performance of our schemes with that of existing schemes. Experiments show that our schemes outperform most existing schemes in both fault tolerance and efficiency.